交换L*-环

我们证明一个交换整环或交换局部环是一个L*-环当且仅当它是一个O*-环.文中还证明了一些一般性的条件使之一个交换环不是L*.     

Linear maps preserving ideals of -algebras

We show that unital self-adjoint linear bijections of matrix algebras, type factors and abelian -algebras preserving maximal left ideals are isomorphisms and we show that a unital continuous linear map of a -algebra that maps the minimal left ideal into itself is the identity map.     

Some remarks on the real rank of non-unital C*-algebras

For a non-unital C-algebra , let be the C-algebra obtained from by adjoining an identity. In this paper we show that

where is a locally compact Hausdorff space with .

     

A novel dual approach to nonlinear semigroups of Lipschitz operators

Lipschitzian semigroup refers to a one-parameter semigroup of Lipschitz operators that is strongly continuous in the parameter. It contains -semigroup, nonlinear semigroup of contractions and uniformly -Lipschitzian semigroup as special cases. In this paper, through developing a series of Lipschitz dual notions, we establish an analysis approach to Lipschitzian semigroup. It is mainly proved that a (nonlinear) Lipschitzian semigroup can be isometrically embedded into a certain -semigroup. As application results, two representation formulas of Lipschitzian semigroup are established, and many asymptotic properties of -semigroup are generalized to Lipschitzian semigroup.

     

极大谱距离的注记

Two equivalent conditions are given for the non-commutative unital C^＊-subalgebras of B（H） algebras A and B to be quantum C^＊ independent.     

Commutative subalgebras of the corona

We use methods of noncommutative functional analysis to extend the range of the usual functional calculus, for certain subalgebras of the corona. In particular, we construct corona projections with interesting properties.

     

Discrete spectra of -algebras and orthogonally closed submodules in Hilbert -modules

Let and be -algebras and let be an --imprimitivity bimodule. Then it is shown that if the spectrum of (resp. of ) is discrete, then every closed --submodule of is orthogonally closed in , and conversely that if (resp. ) is a -space and if every closed --submodule of is orthogonally closed in , then (resp. ) is discrete.

     

Paranormal spaces under

We prove that paranormal spaces of character are -
collectionwise Hausdorff assuming the set-theoretic principle . This gives an affirmative answer to problem 197 in Problems I wish I could solve, by W. S. Watson (Open Problems in Topology (1990), 37-76).

     

Amenability and exactness for dynamical systems and their -algebras

We study the relations between amenability (resp. amenability at infinity) of -dynamical systems and equality or nuclearity (resp. exactness) of the corresponding crossed products.

     

A joint spectral characterization of primeness for C-algebras

We prove that a C-algebra is prime iff for every where denotes Taylor spectrum and are the left and right multiplication operators acting on